Properties

Conductor 2009
Order 35
Real No
Primitive No
Parity Even
Orbit Label 6027.cn

Related objects

Learn more about

Show commands for: SageMath / Pari/GP
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(6027)
 
sage: chi = H[379]
 
pari: [g,chi] = znchar(Mod(379,6027))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 2009
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 35
Real = No
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = No
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = Even
Orbit label = 6027.cn
Orbit index = 66

Galois orbit

sage: chi.sage_character().galois_orbit()
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

\(\chi_{6027}(379,\cdot)\) \(\chi_{6027}(631,\cdot)\) \(\chi_{6027}(652,\cdot)\) \(\chi_{6027}(715,\cdot)\) \(\chi_{6027}(1240,\cdot)\) \(\chi_{6027}(1492,\cdot)\) \(\chi_{6027}(1513,\cdot)\) \(\chi_{6027}(1576,\cdot)\) \(\chi_{6027}(2101,\cdot)\) \(\chi_{6027}(2374,\cdot)\) \(\chi_{6027}(2437,\cdot)\) \(\chi_{6027}(2962,\cdot)\) \(\chi_{6027}(3214,\cdot)\) \(\chi_{6027}(3298,\cdot)\) \(\chi_{6027}(4075,\cdot)\) \(\chi_{6027}(4096,\cdot)\) \(\chi_{6027}(4159,\cdot)\) \(\chi_{6027}(4684,\cdot)\) \(\chi_{6027}(4936,\cdot)\) \(\chi_{6027}(4957,\cdot)\) \(\chi_{6027}(5020,\cdot)\) \(\chi_{6027}(5545,\cdot)\) \(\chi_{6027}(5797,\cdot)\) \(\chi_{6027}(5818,\cdot)\)

Inducing primitive character

\(\chi_{2009}(379,\cdot)\)

Values on generators

\((4019,493,2794)\) → \((1,e\left(\frac{2}{7}\right),e\left(\frac{1}{5}\right))\)

Values

-112458101113161719
\(1\)\(1\)\(e\left(\frac{22}{35}\right)\)\(e\left(\frac{9}{35}\right)\)\(e\left(\frac{24}{35}\right)\)\(e\left(\frac{31}{35}\right)\)\(e\left(\frac{11}{35}\right)\)\(e\left(\frac{1}{35}\right)\)\(e\left(\frac{22}{35}\right)\)\(e\left(\frac{18}{35}\right)\)\(e\left(\frac{26}{35}\right)\)\(e\left(\frac{4}{5}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{35})\)